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- Author or Editor: M. K. Yau x
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Abstract
This study examines the univariate error covariances of hourly rainfall accumulations using two different NWP models and a mosaic of radar reflectivity over a continental-scale domain. The study focuses on two main areas.
The focus of the first part of the paper is on the ensemble-based and the innovation-based error variance and correlation estimations. An ensemble of forecasts and a set of observations provide the basis for estimating the errors in two different ways. The results indicate that both ensemble- and innovation-based methods lead to comparable variance estimations, while the local error correlation estimates have larger differences due to the sensitivity of calculations to the gradient of the variance field.
The second part of the paper uses innovations for identifying the errors. The focus of this part is on a prognostic method for estimating the error statistics from the background based on the Bayesian inference technique. The case study shows that the predictive model produces a similar result regarding the magnitude and the dispersion of variance in comparison with the innovation and ensemble-based variances.
This study represents a step toward estimating local error variances and local error correlations to construct a nonhomogeneous and precipitation-dependent error covariance matrix of rainfall. These results will be used in a future paper in the design of a 2D-VAR Assimilation Method for Blending Extrapolated Radars (AMBER) with NWP precipitation forecast to form a precipitation nowcasting model.
Abstract
This study examines the univariate error covariances of hourly rainfall accumulations using two different NWP models and a mosaic of radar reflectivity over a continental-scale domain. The study focuses on two main areas.
The focus of the first part of the paper is on the ensemble-based and the innovation-based error variance and correlation estimations. An ensemble of forecasts and a set of observations provide the basis for estimating the errors in two different ways. The results indicate that both ensemble- and innovation-based methods lead to comparable variance estimations, while the local error correlation estimates have larger differences due to the sensitivity of calculations to the gradient of the variance field.
The second part of the paper uses innovations for identifying the errors. The focus of this part is on a prognostic method for estimating the error statistics from the background based on the Bayesian inference technique. The case study shows that the predictive model produces a similar result regarding the magnitude and the dispersion of variance in comparison with the innovation and ensemble-based variances.
This study represents a step toward estimating local error variances and local error correlations to construct a nonhomogeneous and precipitation-dependent error covariance matrix of rainfall. These results will be used in a future paper in the design of a 2D-VAR Assimilation Method for Blending Extrapolated Radars (AMBER) with NWP precipitation forecast to form a precipitation nowcasting model.
Abstract
This study presents an information-theoretical score (ITS) with an emphasis on desirable and undesirable mutual information between a series of dichotomous forecast and observation. As ITS makes use of the same contingency table as traditional scores, the performance of threat score (TS), equitable threat score (ETS), and true skill statistics (TSS) are compared with ITS using three different approaches. First, a hypothetical forecast setup is employed to investigate the responses of the scores to bias, phase error, and event frequency. It was found that the desirable mutual information portion of ITS (C +) is closer to TSS, and the undesirable mutual information portion of ITS (C −) reveals the presence of biases and random errors in the forecast. There is also a similarity between ITS and ETS. Second, the sensitivities of ITS and ETS to forecast bias tendency are examined analytically using the critical performance ratio (CPR). It is shown that ITS has a more dynamical response to incremental bias. By increasing the bias, the CPR value of ITS increases more rapidly than that of ETS indicating a higher resistance to hedging. Third, the skill scores on two sets of operational forecasts are applied with respect to a mosaic of observed radar reflectivity. The results show that ITS remains more consistent in its evaluation of skills at different thresholds compared to other scores.
Abstract
This study presents an information-theoretical score (ITS) with an emphasis on desirable and undesirable mutual information between a series of dichotomous forecast and observation. As ITS makes use of the same contingency table as traditional scores, the performance of threat score (TS), equitable threat score (ETS), and true skill statistics (TSS) are compared with ITS using three different approaches. First, a hypothetical forecast setup is employed to investigate the responses of the scores to bias, phase error, and event frequency. It was found that the desirable mutual information portion of ITS (C +) is closer to TSS, and the undesirable mutual information portion of ITS (C −) reveals the presence of biases and random errors in the forecast. There is also a similarity between ITS and ETS. Second, the sensitivities of ITS and ETS to forecast bias tendency are examined analytically using the critical performance ratio (CPR). It is shown that ITS has a more dynamical response to incremental bias. By increasing the bias, the CPR value of ITS increases more rapidly than that of ETS indicating a higher resistance to hedging. Third, the skill scores on two sets of operational forecasts are applied with respect to a mosaic of observed radar reflectivity. The results show that ITS remains more consistent in its evaluation of skills at different thresholds compared to other scores.
Abstract
Abstract
Mesoscale and synoptic-scale analyses were carried out for a severe convective outbreak and two nonsevere convective events in central Alberta. High-resolution upper-air and surface observations gathered during the Limestone Mountain Experiment (LIMEX-85) permitted a detailed diagnosis of the evolution of the atmosphere over the Alberta foothills. On the severe day, deep convection was triggered when upper-level cooling, associated with an advancing, synoptic-scale trough, occurred in phase with strong surface heating over the Alberta foothills from 0800 to 1200 local daylight time (LDT). The deep destabilization over the elevated topography acted to amplify the mountain-plain circulation and to generate mesoscale upslope moisture transport. Concurrently, the surface synoptic pressure gradient gave rise to northeasterly winds that advected a tongue of moist plains air into the lower branch of the mountain-plain circulation. The plains moisture was thus permitted to reach the foothills in time to reinforce the initial convection and effectuate a secondary destabilization. On the nonsevere days, the absence of such joint meso-synoptic-scale upslope moisture transport precluded the occurrence of severe convection.
Abstract
Abstract
Mesoscale and synoptic-scale analyses were carried out for a severe convective outbreak and two nonsevere convective events in central Alberta. High-resolution upper-air and surface observations gathered during the Limestone Mountain Experiment (LIMEX-85) permitted a detailed diagnosis of the evolution of the atmosphere over the Alberta foothills. On the severe day, deep convection was triggered when upper-level cooling, associated with an advancing, synoptic-scale trough, occurred in phase with strong surface heating over the Alberta foothills from 0800 to 1200 local daylight time (LDT). The deep destabilization over the elevated topography acted to amplify the mountain-plain circulation and to generate mesoscale upslope moisture transport. Concurrently, the surface synoptic pressure gradient gave rise to northeasterly winds that advected a tongue of moist plains air into the lower branch of the mountain-plain circulation. The plains moisture was thus permitted to reach the foothills in time to reinforce the initial convection and effectuate a secondary destabilization. On the nonsevere days, the absence of such joint meso-synoptic-scale upslope moisture transport precluded the occurrence of severe convection.
Abstract
An intercomparison of all 11 Limestone Mountain Experiment case days provided the basis for a conceptual model of severe convective outbreaks in Alberta. It is proposed that most severe convective events result when upper-level cooling, associated with an advancing, synoptic-scale trough, occurs in phase with strong surface heating over the Alberta foothills. The deep destabilization over the elevated topography acts to amplify the mountain-plain circulation and to generate mesoscale upslope moisture transport. Concurrently, the surface synoptic pressure gradient gives rise to east-northerly winds that advect the moisture-rich air of the eastern plains into the lower branch of the mountain-plain circulation. In this manner, the plains moisture is permitted to reach the convectively active foothills through underrunning of the capping lid. The end product is the initiation of well-organized, severe convective storms that move eastward with the westerly component of the midtropospheric winds. A statistical analysis based on archived hail data furnished additional evidence for the key synoptic-scale features of the conceptual model.
Abstract
An intercomparison of all 11 Limestone Mountain Experiment case days provided the basis for a conceptual model of severe convective outbreaks in Alberta. It is proposed that most severe convective events result when upper-level cooling, associated with an advancing, synoptic-scale trough, occurs in phase with strong surface heating over the Alberta foothills. The deep destabilization over the elevated topography acts to amplify the mountain-plain circulation and to generate mesoscale upslope moisture transport. Concurrently, the surface synoptic pressure gradient gives rise to east-northerly winds that advect the moisture-rich air of the eastern plains into the lower branch of the mountain-plain circulation. In this manner, the plains moisture is permitted to reach the convectively active foothills through underrunning of the capping lid. The end product is the initiation of well-organized, severe convective storms that move eastward with the westerly component of the midtropospheric winds. A statistical analysis based on archived hail data furnished additional evidence for the key synoptic-scale features of the conceptual model.
Abstract
A mesoscale simulation of the 19–21 July 1996 Saguenay flood cyclone was performed using the Canadian Mesoscale Compressible Community (MC2) model to study the processes leading to the explosive development and the large amount of precipitation. The performance of the simulation is verified by careful comparison with available observations with particular emphasis on the quantitative forecast of precipitation. It was shown that the model accurately simulates the wind, temperature, and humidity fields. Using the Kong and Yau microphysics scheme, the model performs quite well in the threat scores over a broad range of precipitation thresholds. Comparison of model precipitation against an objective analysis from rain gauge measurements and against the time evolution of accumulated precipitation at specific sites indicates generally good agreement except that the magnitude of the maxima is about 10% lower in the simulation.
Potential vorticity (PV) inversion and sensitivity experiments show that the rapid deepening of the cyclone results from a combination of upper-level forcing from two shortwave troughs that partially merge, an upper-level jet streak, latent heat release, and low-level thermal advection. Condensational heating was integral for the establishment of a phase lock between the surface cyclone and a strong, upper-level trough that steers the cyclone. The flow field associated with a weaker trough, located downstream of the stronger trough, acted to retard the progression of the stronger trough, ultimately causing the cyclone to be located in a favorable position to interact with orography. It was shown that in the middle of the explosive deepening period, the contributions to the 900-hPa geopotential height anomaly from the upper-level dry PV anomaly, the low-level moist PV anomaly, and the surface potential temperature anomaly were 47%, 41%, and 12%, respectively.
The contribution to the precipitation from orographic variation is quantified through sensitivity experiments in which aspects of the orography field are altered in the model conditions. It was found that orographic variation contributed to approximately 15% of the 48-h accumulated precipitation in the region of the flooding and up to over 25% in other local areas.
Abstract
A mesoscale simulation of the 19–21 July 1996 Saguenay flood cyclone was performed using the Canadian Mesoscale Compressible Community (MC2) model to study the processes leading to the explosive development and the large amount of precipitation. The performance of the simulation is verified by careful comparison with available observations with particular emphasis on the quantitative forecast of precipitation. It was shown that the model accurately simulates the wind, temperature, and humidity fields. Using the Kong and Yau microphysics scheme, the model performs quite well in the threat scores over a broad range of precipitation thresholds. Comparison of model precipitation against an objective analysis from rain gauge measurements and against the time evolution of accumulated precipitation at specific sites indicates generally good agreement except that the magnitude of the maxima is about 10% lower in the simulation.
Potential vorticity (PV) inversion and sensitivity experiments show that the rapid deepening of the cyclone results from a combination of upper-level forcing from two shortwave troughs that partially merge, an upper-level jet streak, latent heat release, and low-level thermal advection. Condensational heating was integral for the establishment of a phase lock between the surface cyclone and a strong, upper-level trough that steers the cyclone. The flow field associated with a weaker trough, located downstream of the stronger trough, acted to retard the progression of the stronger trough, ultimately causing the cyclone to be located in a favorable position to interact with orography. It was shown that in the middle of the explosive deepening period, the contributions to the 900-hPa geopotential height anomaly from the upper-level dry PV anomaly, the low-level moist PV anomaly, and the surface potential temperature anomaly were 47%, 41%, and 12%, respectively.
The contribution to the precipitation from orographic variation is quantified through sensitivity experiments in which aspects of the orography field are altered in the model conditions. It was found that orographic variation contributed to approximately 15% of the 48-h accumulated precipitation in the region of the flooding and up to over 25% in other local areas.
Abstract
Atmospheric stability properties for cumulus and slantwise convection in oceanic midlatitude cyclones are analyzed using dropsonde observations from the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA). Vertical cross sections perpendicular to the low-level wind shear are selected in the frontal regions for four ERICA storms. To assess the stability properties for conditional symmetric instability (CSI), a sounding analysis is carried out along surfaces of constant absolute angular momentum M. The buoyancy of the parcel along the slanted M surface is determined, both with and without the water loading effect. Our analysis suggests that a systematic bias toward overestimation of slantwise instability occurs when the loading effect is neglected.
The major finding of our analysis is that the lower-tropospheric air on the warm side of the warm-frontal zone is stable or neutral with respect to vertical cumulus convection but unstable for slantwise convection. Convective instability, however, is found in the warm sector near the surface low of explosive cyclones during their period of most rapid growth. Our analysis shows that conditional slantwise instability, throughout a deep layer, can occur even in a slowly developing cyclone. Observed precipitation events were consistent with the occurrence of slantwise and cumulus convection.
Abstract
Atmospheric stability properties for cumulus and slantwise convection in oceanic midlatitude cyclones are analyzed using dropsonde observations from the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA). Vertical cross sections perpendicular to the low-level wind shear are selected in the frontal regions for four ERICA storms. To assess the stability properties for conditional symmetric instability (CSI), a sounding analysis is carried out along surfaces of constant absolute angular momentum M. The buoyancy of the parcel along the slanted M surface is determined, both with and without the water loading effect. Our analysis suggests that a systematic bias toward overestimation of slantwise instability occurs when the loading effect is neglected.
The major finding of our analysis is that the lower-tropospheric air on the warm side of the warm-frontal zone is stable or neutral with respect to vertical cumulus convection but unstable for slantwise convection. Convective instability, however, is found in the warm sector near the surface low of explosive cyclones during their period of most rapid growth. Our analysis shows that conditional slantwise instability, throughout a deep layer, can occur even in a slowly developing cyclone. Observed precipitation events were consistent with the occurrence of slantwise and cumulus convection.
Abstract
Seven precipitation bands observed during the Canadian Atlantic Storms Program (CASP) are studied to assess the importance of slantwise convective instability. Using three-hourly radiosonde data from regular and special stations, vertical cross sections of θ e *(saturated equivalent potential temperature) and M,(absolute angular momentum) and θe(equivalent potential temperature) and M surfaces are constructed. A comparison of the slopes of constant M,θe and θ e * surfaces indicates the presence of potential and conditional slantwise instability. This study focuses on the time evolution of the stability field and on the adjustment to its neutral state.
Consistent results were found in seven cases analyzed. The atmosphere is shown to contain shallow layers of air that are slightly unstable for conditional slantwise convection, particularly in regions having pronounced windshear. In the upper levels, the potential for instability usually remains only a potential because the lack of moisture precludes the actual release of energy. On the other hand, in the lower part of the atmosphere saturation is often realized and the instability is released leading to heavy precipitation which is sometimes organized in multiple bands. Our results also demonstrate that the atmosphere is undergoing an adjustment toward a state of conditional neutrality with respect to slantwise convection in saturated regions. The adjustment time of less than three hours is consistent with Enianuel's hypothesis of rapid adjustment.
Abstract
Seven precipitation bands observed during the Canadian Atlantic Storms Program (CASP) are studied to assess the importance of slantwise convective instability. Using three-hourly radiosonde data from regular and special stations, vertical cross sections of θ e *(saturated equivalent potential temperature) and M,(absolute angular momentum) and θe(equivalent potential temperature) and M surfaces are constructed. A comparison of the slopes of constant M,θe and θ e * surfaces indicates the presence of potential and conditional slantwise instability. This study focuses on the time evolution of the stability field and on the adjustment to its neutral state.
Consistent results were found in seven cases analyzed. The atmosphere is shown to contain shallow layers of air that are slightly unstable for conditional slantwise convection, particularly in regions having pronounced windshear. In the upper levels, the potential for instability usually remains only a potential because the lack of moisture precludes the actual release of energy. On the other hand, in the lower part of the atmosphere saturation is often realized and the instability is released leading to heavy precipitation which is sometimes organized in multiple bands. Our results also demonstrate that the atmosphere is undergoing an adjustment toward a state of conditional neutrality with respect to slantwise convection in saturated regions. The adjustment time of less than three hours is consistent with Enianuel's hypothesis of rapid adjustment.
Abstract
The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments.
From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process.
From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.
Abstract
The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments.
From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process.
From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.
Abstract
Highly asymmetric structures in a landfalling hurricane can lead to the formation of heavy rains, wind gusts, and tornados at prefered locations relative to the center of the hurricane. In this study, the development of asymmetric structures in an explicitly simulated idealized hurricane during landfall was investigated.
It was found that the boundary layer friction and its associated convection produce a low-level positive potential vorticity (PV) band ahead of the hurricane. The interaction between the PV band and the eyewall PV ring leads to a temporary weakening and reintensifying cycle. Asymmetric structures arise from the near discontinuity of the surface friction and the latent heat flux. The breaking of the eyewall in the rear quadrants is favorable for the intrusion of the low moist entropy air into the core. Consequently, PV increases significantly in the core, in and just above the boundary layer due to the stabilization. After the hurricane makes landfall, the diabatic heating in the eyewall is reduced and cannot generate enough PV to maintain the PV ring in the middle and upper troposphere. The PV ring evolves into a monopolar structure through the nonlinear mixing process.
The Eliassen–Palm (EP) flux and its divergence in the Eulerian mean equations in isentropic coordinates are applied to explore the wave dynamics and wave–mean flow interactions. The vortex Rossby wave–related eddy momentum and heat transports, indicated by the EP flux, vary as a response to the evolution of the PV structure. The wave–mean flow interaction has a significant effect on the tangential wind, which is dominated by the mean circulation, especially the symmetric diabatic heating. Together with the asymmetric diabatic heating, the waves tend to counteract the effect of the mean circulation.
Abstract
Highly asymmetric structures in a landfalling hurricane can lead to the formation of heavy rains, wind gusts, and tornados at prefered locations relative to the center of the hurricane. In this study, the development of asymmetric structures in an explicitly simulated idealized hurricane during landfall was investigated.
It was found that the boundary layer friction and its associated convection produce a low-level positive potential vorticity (PV) band ahead of the hurricane. The interaction between the PV band and the eyewall PV ring leads to a temporary weakening and reintensifying cycle. Asymmetric structures arise from the near discontinuity of the surface friction and the latent heat flux. The breaking of the eyewall in the rear quadrants is favorable for the intrusion of the low moist entropy air into the core. Consequently, PV increases significantly in the core, in and just above the boundary layer due to the stabilization. After the hurricane makes landfall, the diabatic heating in the eyewall is reduced and cannot generate enough PV to maintain the PV ring in the middle and upper troposphere. The PV ring evolves into a monopolar structure through the nonlinear mixing process.
The Eliassen–Palm (EP) flux and its divergence in the Eulerian mean equations in isentropic coordinates are applied to explore the wave dynamics and wave–mean flow interactions. The vortex Rossby wave–related eddy momentum and heat transports, indicated by the EP flux, vary as a response to the evolution of the PV structure. The wave–mean flow interaction has a significant effect on the tangential wind, which is dominated by the mean circulation, especially the symmetric diabatic heating. Together with the asymmetric diabatic heating, the waves tend to counteract the effect of the mean circulation.
Abstract
An initially axisymmetric hurricane was explicitly simulated using the high-resolution PSU–NCAR nonhydrostatic mesoscale model (MM5). Spiral potential vorticity (PV) bands that formed in the model were analyzed. It was shown that PV bands and cloud bands are strongly coupled. The PV anomalies in and at the top of the boundary layer interact with friction to produce upward motion that gives rise to the inner cloud bands. The propagation properties of the PV bands were studied and found to be consistent with predictions of vortex Rossby wave theory.
In the control simulation with full physics, continuous generation of PV through latent heat release in the eyewall and spiral rainbands maintain a “bowl-shape” PV field. Inward transport of high PV by the vortex Rossby waves and the process of nonlinear mixing tend to increase the inner-core PV and in turn intensify the hurricane. On the other hand, frictional and PV mixing processes acted linearly to spin down the hurricane to a midlevel vortex in a dry run, which indicates that a monopolar PV structure is the asymptotic stable state in the absence of condensation.
Abstract
An initially axisymmetric hurricane was explicitly simulated using the high-resolution PSU–NCAR nonhydrostatic mesoscale model (MM5). Spiral potential vorticity (PV) bands that formed in the model were analyzed. It was shown that PV bands and cloud bands are strongly coupled. The PV anomalies in and at the top of the boundary layer interact with friction to produce upward motion that gives rise to the inner cloud bands. The propagation properties of the PV bands were studied and found to be consistent with predictions of vortex Rossby wave theory.
In the control simulation with full physics, continuous generation of PV through latent heat release in the eyewall and spiral rainbands maintain a “bowl-shape” PV field. Inward transport of high PV by the vortex Rossby waves and the process of nonlinear mixing tend to increase the inner-core PV and in turn intensify the hurricane. On the other hand, frictional and PV mixing processes acted linearly to spin down the hurricane to a midlevel vortex in a dry run, which indicates that a monopolar PV structure is the asymptotic stable state in the absence of condensation.
